Question
Solve and check the linear equation. \[ 3(x-3)+12=2(x+4) \] What is the solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \} \). B. The solution set is \( \{x \mid x \) is a real number \( \} \). C. The solution set is \( \varnothing \).
Ask by Erickson Ryan. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( x = 5 \).
Solution
We start with the equation:
3(x - 3) + 12 = 2(x + 4).
Step 1: Distribute on both sides.
Left side: 3x - 9 + 12 = 3x + 3.
Right side: 2x + 8.
Step 2: Set the equation:
3x + 3 = 2x + 8.
Step 3: Subtract 2x from both sides:
x + 3 = 8.
Step 4: Subtract 3 from both sides:
x = 5.
Check:
Substitute x = 5 back into the original equation:
3(5 - 3) + 12 = 3(2) + 12 = 6 + 12 = 18,
2(5 + 4) = 2(9) = 18.
Both sides equal 18, confirming that x = 5 is correct.
Thus, the solution set is {5}.
The correct choice is:
A. The solution set is {5}.
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Simplify this solution Extra Insights
To solve the equation \( 3(x-3)+12=2(x+4) \), we first distribute and simplify both sides: 1. Distribute on the left: \( 3x - 9 + 12 = 2(x + 4) \) becomes \( 3x + 3 = 2x + 8 \). 2. Next, isolate x: Subtract \( 2x \) from both sides, resulting in \( x + 3 = 8 \). 3. Then, subtract 3 from both sides: \( x = 5 \). Now let's check our solution by substituting \( x = 5 \) back into the original equation: Left side: \( 3(5-3)+12 = 3(2)+12 = 6 + 12 = 18 \). Right side: \( 2(5+4) = 2(9) = 18 \). Both sides are equal, confirming that \( x = 5 \) is the correct solution. So, the solution set is: A. The solution set is \( \{5\} \).
